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Articles 31 - 36 of 36
Full-Text Articles in Partial Differential Equations
On A Class Of Backward Mckean-Vlasov Stochastic Equations In Hilbert Space: Existence And Convergence Properties, Nazim I. Mahmudov, Mark A. Mckibben
On A Class Of Backward Mckean-Vlasov Stochastic Equations In Hilbert Space: Existence And Convergence Properties, Nazim I. Mahmudov, Mark A. Mckibben
Mathematics Faculty Publications
This investigation is devoted to the study of a class of abstract first-order backward McKean-Vlasov stochastic evolution equations in a Hilbert space. Results concerning the existence and uniqueness of solutions and the convergence of an approximating sequence of solutions (and corresponding probability measures) are established. Examples that illustrate the abstract theory are also provided.
On Backward Stochastic Evolution Equations In Hilbert Space And Optimal Control, Nazim I. Mahmudov, Mark A. Mckibben
On Backward Stochastic Evolution Equations In Hilbert Space And Optimal Control, Nazim I. Mahmudov, Mark A. Mckibben
Mathematics Faculty Publications
In this paper a new result on the existence and uniqueness of the adapted solution to a backward stochastic evolution equation in Hilbert spaces under non Lipschitz condition is established. The applicability of this result is then illustrated in a discussion of some concrete backward stochastic partial differential equation. Furthermore, stochastic maximum principle for optimal control problems of stochastic systems governed by backward stochastic evolution equations in Hilbert spaces is obtained.
Abstract Semilinear Itó-Volterra Integro-Differential Stochastic Evolution Equations, David N. Keck, Mark A. Mckibben
Abstract Semilinear Itó-Volterra Integro-Differential Stochastic Evolution Equations, David N. Keck, Mark A. Mckibben
Mathematics Faculty Publications
We consider a class of abstract semilinear stochastic Volterra integrodifferential equations in a real separable Hilbert space. The global existence and uniqueness of a mild solution, as well as a perturbation result, are established under the so-called Caratheodory growth conditions on the nonlinearities. An approximation result is then established, followed by an analogous result concerning a so-called McKean-Vlasov integrodi fferential equation, and then a brief commentary on the extension of the main results to the time-dependent case. The paper ends with a discussion of some concrete examples to illustrate the abstract theory.
Abstract Second-Order Damped Mckean-Vlasov Stochastic Evolution Equations, N. I. Mahmudov, Mark A. Mckibben
Abstract Second-Order Damped Mckean-Vlasov Stochastic Evolution Equations, N. I. Mahmudov, Mark A. Mckibben
Mathematics Faculty Publications
We establish results concerning the global existence, uniqueness, approximate and exact controllability of mild solutions for a class of abstract second-order stochastic evolution equations in a real separable Hilbert space in which we allow the nonlinearities at a given time t to depend not only on the state of the solution at time t, but also on the corresponding probability distribution at time t. First-order equations of McKean-Vlasov type were first analyzed in the finite dimensional setting when studying diffusion processes, and then subsequently extended to the Hilbert space setting. The current manuscript provides a formulation of such …
On State-Dependent Delay Partial Neutral Functional–Differential Equations, Eduardo Hernandez M., Mark A. Mckibben
On State-Dependent Delay Partial Neutral Functional–Differential Equations, Eduardo Hernandez M., Mark A. Mckibben
Mathematics Faculty Publications
No abstract provided.
Some Comments On: Existence Of Solutions Of Abstract Nonlinear Second-Order Neutral Functional Integrodifferential Equations, Eduardo Hernandez, Mark A. Mckibben
Some Comments On: Existence Of Solutions Of Abstract Nonlinear Second-Order Neutral Functional Integrodifferential Equations, Eduardo Hernandez, Mark A. Mckibben
Mathematics Faculty Publications
We establish the existence of mild solutions for a class of abstract second-order partial neutral functional integro-differential equations with infinite delay in a Banach space using the theory of cosine families of bounded linear operators and Schaefer's fixed-point theorem.